Aerodynamic forces and moments on an insect-like flapping wing in forward flight were measured to explore the aerodynamic characteristics depending on advance ratios J. To this end, we developed a three-rotational DOF robotic wing model being able to travel to the longitudinal direction by the servo-driven towing tank. In hovering (J=0), the wing generated the identical amount of the aerodynamic force and pitching moment during each upstroke and downstroke, because of a symmetric motion profile. As J increases, the wing in downstroke produced most of lift force, which is enough to stay aloft, and the force in upstroke tilts toward the forward direction. A geometrical relationship based on the global coordinate well explained those changes with respect to the J. However, the quasi-steady model including such geometrical relationship does not show a good agreement with the measurements, and the differences are gradually increased with respect to the J. These imply that the increase in J brings on the change of the fundamental aerodynamic characteristics, and indicate that the aerodynamic model should be compensated for by including the J effect.